-gap functions and descent methods for a class of monotone equilibrium problems.
Decomposition of large-scale stochastic optimal control problems
In this paper, we present an Uzawa-based heuristic that is adapted to certain type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale subsystems linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, for instance, power units, and one has to supply a stochastic power demand at each time step. We outline the framework...
Differential evolution algorithm combined with chaotic pattern search
Differential evolution algorithm combined with chaotic pattern search(DE-CPS) for global optimization is introduced to improve the performance of simple DE algorithm. Pattern search algorithm using chaotic variables instead of random variables is used to accelerate the convergence of solving the objective value. Experiments on 6 benchmark problems, including morbid Rosenbrock function, show that the novel hybrid algorithm is effective for nonlinear optimization problems in high dimensional space....
Dimension reduction for −Δ1
A 3D-2D dimension reduction for −Δ1 is obtained. A power law approximation from −Δp as p → 1 in terms of Γ-convergence, duality and asymptotics for least gradient functions has also been provided.
Direct method for variational problems via hybrid of block-pulse and Chebyshev functions.
Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions
In this paper, a new numerical method for solving the nonlinear constrained optimal control with quadratic performance index is presented. The method is based upon B-spline functions. The properties of B-spline functions are presented. The operational matrix of derivative () and integration matrix () are introduced. These matrices are utilized to reduce the solution of nonlinear constrained quadratic optimal control to the solution of nonlinear programming one to which existing well-developed...
Direct variational methods in nonreflexive spaces
Directional lipschitzian optimal solutions and directional derivative for the optimal value function in nonlinear mathematical programming
Discrete dynamic programming and viscosity solutions of the Bellman equation
Discrete mechanics and optimal control: An analysis
The optimal control of a mechanical system is of crucial importance in many application areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be performed in order to make the problem amenable to computations. The approach proposed in this paper...
Discrete mechanics and optimal control: An analysis*
The optimal control of a mechanical system is of crucial importance in many application areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be performed in order to make the problem amenable to computations. The approach proposed in this paper...
Discrete optimal control problems with nonsmooth costs
Discrete periodic geodesics in a surface.
Duality based a posteriori error estimates for higher order variational inequalities with power growth functionals.
Duality theory in mathematical programming and optimal control
Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities
A dual-weighted residual approach for goal-oriented adaptive finite elements for a class of optimal control problems for elliptic variational inequalities is studied. The development is based on the concept of C-stationarity. The overall error representation depends on primal residuals weighted by approximate dual quantities and vice versa as well as various complementarity mismatch errors. Also, a priori bounds for C-stationary points and associated multipliers are derived. Details on the numerical...
Dykstra's algorithm as the nonlinear extension of Bregman's optimization method.
Dynamic optimal cooling control for continuous casting of steel